Stereo Array Positioning Algorithm Based on Vector Projection
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摘要: 传统适配立体阵型的超短基线定位算法计算量大、定位误差难以通过解析式精确表征。针对这些问题，该文提出基于向量投影的立体阵定位算法，从向量投影的角度构建立体阵中各基线向量与目标方位之间的观测方程，实现对传统算法定位模型的简化。该文算法通过求解线性方程组即可实现对目标方位的估计，时间复杂度远小于传统算法。此外，基于该文算法简洁的观测方程，给出了适配立体阵的定位误差精确解析表征。仿真结果表明，该文算法消耗的运算时间远小于传统算法，且定位误差变化规律与基于理论解析式得到的结论相符。湖试试验结果表明，该文算法的定位精度与传统算法几乎一致，且计算效率更高。Abstract: The traditional ultra-short baseline positioning algorithm for stereo arrays exhibits high computational complexity and struggles to accurately represent the positioning error through an explicit formula. To address these challenges, a stereo array positioning algorithm based on vector projection is proposed. The observation equations between the baseline vectors in the stereo array and the target bearing were constructed based on the vector projection theorem, simplifying the positioning model of the traditional algorithm. In the proposed algorithm, the target bearing is obtained by solving a system of linear equations, which results in lower time complexity. Additionally, an accurate analytical representation of the positioning error applicable to the stereo array is provided based on the concise observation equations of the proposed algorithm. The simulation results show that the computational time required by the proposed algorithm is significantly lower compared to the traditional algorithm, and the variation pattern of the positioning error is consistent with the conclusion drawn from the theoretical analysis. The experimental results further indicate that the proposed algorithm achieves almost the same positioning accuracy but higher computation efficiency comparable to the traditional algorithm.
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Key words:
- Ultra-short baseline positioning /
- Stereo array /
- Vector projection
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表 1 算法均方根误差及运行时间统计结果
算法名称 北向均方根误差(m) 东向均方根误差(m) 天向均方根误差(m) 运行时间(s) 三角分解算法 0.2048 0.2244 0.6600 0.1225 向量投影算法 0.1714 0.1752 0.6561 0.0131 
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